Answer
The difference between a circle and a parabola is that circles are of the form $x^2+y^2=z^2$ (where $z\ne0$) and parabolas are of the form $y=x^2$ or $y^2=x$. (Both parabolas and circles can be shifted any number of units from the origin.)
Work Step by Step
Upward and downward parabolas are of the form $x^2=y$, while left-opening and right-opening parabolas are of the form $x=y^2$.
